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Thomas' Calculus, 11/E
George B. Thomas, Jr., Massachusetts Institute of Technology
Maurice D. Weir, Naval Postgraduate School
Joel Hass, University of California, Davis
Frank R. Giordano, Naval Postgraduate School

ISBN-10: 0321185587
ISBN-13: 9780321185587

Publisher: Addison-Wesley
Copyright: 2005
Format: Cloth; 1380 pp
Status: Out of Print

Suggested retail price: $165.33
This item is out of print and is no longer available for purchase.

The new edition of Thomas is a return to what Thomas has always been: the book with the best exercises. For the 11th edition, the authors have added exercises cut in the 10th edition, as well as, going back to the classic 5th and 6th editions for additional exercises and examples.

The book's theme is that Calculus is about thinking; one cannot memorize it all. The exercises develop this theme as a pivot point between the lecture in class, and the understanding that comes with applying the ideas of Calculus.

In addition, the table of contents has been refined to match the standard syllabus. Many of the examples have been trimmed of distractions and rewritten with a clear focus on the main ideas. The authors have also excised extraneous information in general and have made the technology much more transparent.

The ambition of Thomas 11e is to teach the ideas of Calculus so that students will be able to apply them in new and novel ways, first in the exercises but ultimately in their careers. Every effort has been made to insure that all content in the new edition reinforces thinking and encourages deep understanding of the material.

  • Carefully developed exercises — the benchmark by which all other books are measured.
  • Applications to the physical world — a Thomas trademark.
  • Transparent integration of technology.
  • Complete and careful multivariable calculus section.
  • Online resources including exercises and projects.
  • Streamlined coverage of the techniques of integration.

  • The 11th edition is based on the strengths of the 5th, 6th, and 9th Editions of Thomas' Calculus.
  • New chapter on integration. Integration introduced through finite sums; indefinite integrals follow the Fundamental Theorem.
  • Proofs have been pulled out of the appendix and placed back in the body of the book. Emphasis on mathematical precision and rigor throughout, including proofs of most major results. Care is taken to point out where proofs are given and where omitted.
  • Combined treatment of 2- and 3-dimensional vectors; a single chapter on vector-valued functions.
  • Brief new appendix on the theory of real numbers emphasizing its role in calculus.
  • Limits are covered both intuitively and precisely.

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)

Preliminaries.

Real Numbers and the Real Line.

Lines, Circles, and Parabolas.

Functions and Their Graphs.

Identifying Functions; Mathematical Models.

Combining Functions; Shifting and Scaling Graphs.

Trigonometric Functions.

Graphing with Calculators and Computers.



2. Limits and Derivatives.

Rates of Change and Limits.

Calculating Limits Using the Limit Laws.

Precise Definition of a Limit.

One-Sided Limits and Limits at Infinity.

Infinite Limits and Vertical Asymptotes.

Continuity.

Tangents and Derivatives.



3. Differentiation.

The Derivative as a Function.

Differentiation Rules.

The Derivative as a Rate of Change.

Derivatives of Trigonometric Functions.

The Chain Rule and Parametric Equations.

Implicit Differentiation.

Related Rates.

Linearization and Differentials.



4. Applications of Derivatives.

Extreme Values of Functions.

The Mean Value Theorem.

Monotonic Functions and the First Derivative Test.

Concavity and Curve Sketching.

Applied Optimization Problems.

Indeterminate Forms and L'Hopital's Rule.

Newton's Method.

Antiderivatives.



5. Integration.

Estimating with Finite Sums.

Sigma Notation and Limits of Finite Sums.

The Definite Integral.

The Fundamental Theorem of Calculus.

Indefinite Integrals and the Substitution Rule.

Substitution and Area Between Curves.



6. Applications of Definite Integrals.

Volumes by Slicing and Rotation About an Axis.

Volumes by Cylindrical Shells.

Lengths of Plane Curves.

Moments and Centers of Mass.

Areas of Surfaces of Revolution and The Theorems of Pappus.

Work.

Fluid Pressures and Forces.



7. Transcendental Functions.

Inverse Functions and their Derivatives.

Natural Logarithms.

The Exponential Function.

ax and loga x.

Exponential Growth and Decay.

Relative Rates of Growth.

Inverse Trigonometric Functions.

Hyperbolic Functions.



8. Techniques of Integration.

Basic Integration Formulas.

Integration by Parts.

Integration of Rational Functions by Partial Fractions.

Trigonometric Integrals.

Trigonometric Substitutions.

Integral Tables and Computer Algebra Systems.

Numerical Integration.

Improper Integrals.



9. Further Applications of Integration.

Slope Fields and Separable Differential Equations.

First-Order Linear Differential Equations.

Euler's Method.

Graphical Solutions of Autonomous Equations.

Applications of First-Order Differential Equations.



10. Conic Sections and Polar Coordinates.

Conic Sections and Quadratic Equations .

Classifying Conic Sections by Eccentricity.

Quadratic Equations and Rotations.

Conics and Parametric Equations; The Cycloid.

Polar Coordinates .

Graphing in Polar Coordinates.

Area and Lengths in Polar Coordinates.

Conic Sections in Polar Coordinates.



11. Infinite Sequences and Series.

Sequences.

Infinite Series.

The Integral Test.

Comparison Tests.

The Ratio and Root Tests.

Alternating Series, Absolute and Conditional Convergence.

Power Series.

Taylor and Maclaurin Series.

Convergence of Taylor Series; Error Estimates.

Applications of Power Series.

Fourier Series.



12. Vectors and the Geometry of Space.

Three-Dimensional Coordinate Systems.

Vectors.

The Dot Product.

The Cross Product.

Lines and Planes in Space.

Cylinders and Quadric Surfaces .



13. Vector-Valued Functions and Motion in Space.

Vector Functions.

Modeling Projectile Motion.

Arc Length and the Unit Tangent Vector T.

Curvature and the Unit Normal Vector N.

Torsion and the Unit Binormal Vector B.

Planetary Motion and Satellites.



14. Partial Derivatives.

Functions of Several Variables.

Limits and Continuity in Higher Dimensions.

Partial Derivatives.

The Chain Rule.

Directional Derivatives and Gradient Vectors.

Tangent Planes and Differentials.

Extreme Values and Saddle Points.

Lagrange Multipliers.

*Partial Derivatives with Constrained Variables.

Taylor's Formula for Two Variables.



15. Multiple Integrals.

Double Integrals.

Areas, Moments and Centers of Mass*.

Double Integrals in Polar Form.

Triple Integrals in Rectangular Coordinates.

Masses and Moments in Three Dimensions.

Triple Integrals in Cylindrical and Spherical Coordinates.

Substitutions in Multiple Integrals.



16. Integration in Vector Fields.

Line Integrals.

Vector Fields, Work, Circulation, and Flux.

Path Independence, Potential Functions, and Conservative Fields.

Green's Theorem in the Plane.

Surface Area and Surface Integrals.

Parametrized Surfaces.

Stokes' Theorem.

The Divergence Theorem and a Unified Theory.



Appendices.

Mathematical Induction.

Proofs of Limit Theorems.

Commonly Occurring Limits .

Theory of the Real Numbers.

Complex Numbers.

The Distributive Law for Vector Cross Products.

Determinants and Cramer's Rule.

The Mixed Derivative Theorem and the Increment Theorem.

The Area of a Parallelogram's Projection on a Plane.

View a Sample Chapter PDF:

 

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This title is a member of the Thomas Series, which also contains the titles below . You can also visit the Thomas Series page.

    Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level.  However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas’ Calculus Early Transcendentals, Part One, Media Upgrade, Eleventh Edition responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course. 

     

    Thomas’ Calculus Early Transcendentals, Part One, Media Upgrade, Eleventh Edition is now available with an enhanced MyMathLab™ course—the ultimate homework, tutorial and study solution for today’s students.  The enhanced MyMathLab™ course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL® exercises.  This text is also available with WebAssign® and WeBWorK®.

  • 0321498747Thomas' Calculus, Early Transcendentals, Media Upgrade, Part One, 11/E
    Thomas, Weir, Hass & Giordano
    © 2008 | Addison-Wesley | Paper; 864 pages | Instock
    ISBN-10: 0321498747 | ISBN-13: 9780321498748
    Brief Description | Buy from myPearsonStore

    • <>Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level.  However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas’ Calculus, Media Upgrade, Eleventh Edition, Part One responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course. 

     

    Thomas’ Calculus, Media Upgrade, Eleventh Edition, Part One is now available with an enhanced MyMathLab™ course–the ultimate homework, tutorial and study solution for today’s students.  The enhanced MyMathLab course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL® exercises.  This text is also available with WebAssign® and WeBWorK®.

  • 0321498755Thomas' Calculus, Media Upgrade, Part One (Single Variable), 11/E
    Thomas, Weir, Hass & Giordano
    © 2008 | Addison-Wesley | Paper; 864 pages | Instock
    ISBN-10: 0321498755 | ISBN-13: 9780321498755
    Brief Description | Buy from myPearsonStore

    • Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level.  However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas’ Calculus, Media Upgrade, Eleventh Edition, Part Two responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course. 

     

    Thomas’ Calculus, Media Upgrade, Eleventh Edition, Part Two is now available with an enhanced MyMathLab™ course—the ultimate homework, tutorial and study solution for today’s students.  The enhanced MyMathLab course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL® exercises.  This text is also available with WebAssign® and WeBWorK®.

  • 0321501039Thomas' Calculus, Media Upgrade, Part Two (Multivariable, Chap 11-16), 11/E
    Thomas, Weir, Hass & Giordano
    © 2008 | Addison-Wesley | Paper | Instock
    ISBN-10: 0321501039 | ISBN-13: 9780321501035
    Brief Description | Buy from myPearsonStore

    • This streamlined version of ‘Thomas’ Calculus’ provides a faster-paced, precise and accurate presentation of calculus for a college-level calculus course. ‘University Calculus’ covers both single variable and multivariable calculus and is appropriate for a three semester or four quarter course.

     

    University Calculus is the ideal choice for professors who want a faster-paced text with a more conceptually balanced exposition.  It is a blend of intuition and rigor.  Transcendental functions are introduced early, and are continually revisited in more depth in subsequent chapters of the text

  • 0321350146University Calculus
    Hass, Weir & Thomas
    © 2007 | Addison-Wesley | Cloth; 930 pages | Instock
    ISBN-10: 0321350146 | ISBN-13: 9780321350145
    Brief Description | Buy from myPearsonStore

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